Cosmology and Computing

Classical Transitions

The inflationary paradigm has no single, compelling theoretical motivation. One possible approach to its explanation involves invoking string theory; where many degrees of freedom provide an effective field theory of high dimension and complication. This is known as the string landscape (see e.g. (Polchinski:2006gy) for a review) because the existence of an (increasing) large number of meta stable vacuua. Each vacuum has a different energy density and drives expansion at a different rate.

Each vacuum state, $i$, has an associated vacuum energy, V_i, which can, in principle range over many orders of magnitude. If a region of spactime is within one of these metastable vacuua, say, 1, it would undergo deSitter expansion at a rate of H_1∝ √V_1/m_pl. It has been known for quite some time that regions of spacetime can quantum mechanically tunnel to a region V_2 where V_2 < V_1 (Coleman:1980aw). This ``bubble universe" would then expand, its walls quickly approaching the speed of light. However, the expansion rate inside the bubble, H_2∝ √V_2/m_pl is, by construction, less than the expansion rate of the bulk space. So long as this tunneling rate is slow, there will always be some volume of space in state 1, hence the name eternal inflation.

The probability of tunneling is a statistical process. But there will always be collisions between bubbles. To stay with the analogy presented above, it is possible for two bubbles of vacuum 2 to nucleate in the bulk of vacuum 1. Under general circumstances that will inevitably occur, these bubbles will collide. Such collisions have inspired investigation for decades, starting with numerical simulations of the collisions themselves (Hawking:1982ga), with searches for gravitational radiation (Kosowsky:1991ua, Aguirre:2009), and other observational consequences (Chang:2007eq, Aguirre:2007an, Aguirre:2007anwm).

The discovery of classical transitions occurring during bubble collisions opens up a larger question about the phenomenally of these collisions (Easther:2009ft, Giblin:2010bd). These models use simple polynomials to realize potentials with many minima. These models are but a representation and must, eventually, be replaced by the better motivated, string theory models of (Aguirre:2009tp, BlancoPillado:2010df).